Table of contents

A mechanism, based on the dependence of the anomalous plasma viscosity on the velocity gradient, is proposed to explain a strong shearing of the ion toroidal velocity in the radiatively improved (RI) mode in TEXTOR-94 with unbalanced neutral injection. The conditions of the bifurcation into this plasma state with a barrier in the ion momentum and heat transport are analysed, and it is demonstrated that the density peaking caused by puffing of impurities is of principal importance to achieve them. The time evolution of the ion toroidal velocity and temperature by the transition into the RI mode is modelled.

Tungsten was injected by means of laser ablation in both ohmic and additionally heated plasmas of the ASDEX Upgrade tokamak experiment. Spectroscopic investigations were performed in the extreme ultraviolet (EUV) wavelength region, 4 to 140 nm. Besides the quasi-continuum structure at ≈ 5 nm emitted by tungsten ions around W²⁷⁺, isolated lines of tungsten were observed in the same spectral region and also in the range from 12 to 14 nm. By comparison with calculations from the HULLAC and RELAC codes, these lines could be identified as transitions of bromine to nickel-like tungsten ions. The concentration c_W of tungsten after laser ablation was determined from comparisons between the total tungsten radiation P_W and the calculated radiation losses. Calibration of the quasi-continuum intensity with the help of the P_W measurements allows the tungsten concentration to be determined from spectroscopic observations, which are more sensitive. Both concentration measurements (quasi-continuum, P_W) agree well in discharges with laser ablation. From a comparison of the intensity of the isolated lines with code results, c_W could be estimated in the central region of hot, additionally heated plasmas. The lower detection limit of the spectroscopic method allows the extraction of c_W during the tungsten divertor experiment of ASDEX Upgrade.

At sufficiently high poloidal beta β_θ and low collisionality, m/n = 3/2 tearing modes are excited in the DIII-D tokamak by a q = 1 sawtooth crash perturbation. The resulting islands of full radial width w are long lived and reduce global confinement (and β_θ) by up to 30%. These are tearing modes produced by the perturbed neoclassical bootstrap current destabilization of a seed island arising from the m/n = 2/2 sawtooth precursor. The tearing modes are metastable. Even if the modes are conventionally stable, i.e. Δ^' < 0, for sufficiently high β_θ, there is a range of island widths w above some threshold value over which the modified Rutherford equation predicts island growth. This threshold value increases with collisionality. Both `transport' and `polarization' threshold models are compared with experiment. The transport model gives the correct scaling with experiment, but the threshold island w_d is 3 to 9 times too small, depending on whether ion or electron parallel heat transport is used. The polarization model threshold island w_g gives good agreement with experiment, utilizing an approximately hyperbolic tangent transition from collisionless to collisional regimes.

Drift orbit topologies in the H-1NF heliac are described using guiding centre calculations and by the approximate second adiabatic invariant. Results are presented that are representative of the orbit topologies across the magnetic configuration space of the machine and in the presence of radial electric fields. The trapped particle population can be divided into a number of different subclasses using a scheme based on the number of maxima in parallel kinetic energy between bounce points.

A new model based on a combination of a Bohm-like term plus a gyro-Bohm-like term is proposed for the electron and ion heat diffusivity in the L mode regime, which is the commonest regime of operation of tokamaks. This model is derived using the dimensionless analysis technique taking into account the indications of scaling laws for the global confinement time and other experimental constraints on the diffusivity. The model has been successfully tested against data from several different experiments from the ITER database and the local Tore Supra database. Statistical analysis has shown it to perform better than purely Bohm or gyro-Bohm models and global scaling laws in the chosen dataset.

The characteristics of external kink instabilities observed during wall stabilization studies in the HBT-EP tokamak have been compared with the predictions of ideal MHD theory, in order to examine the stabilizing role of a resistive wall that is segmented both toroidally and poloidally. The reconstructed equilibria, for discharges with different plasma-wall configurations, are consistent with external and internal magnetic measurements, measured soft X ray profiles and measured equilibrium wall eddy currents. The stability analysis of these equilibria predicts patterns of instability induced eddy currents for a model wall that is continuous and perfectly conducting, and these patterns are in good agreement with the ones observed on the HBT-EP segmented wall. These eddy currents account for the observed stabilization of fast ideal modes when the wall is fully inserted, consistent with the prediction of marginal stability.

The response of ohmic, single null diverted (SND), non-centred plasmas in TCV to poloidal field coil stimulation has been compared with the predictions of the linear CREATE-L MHD equilibrium response model. The closed loop responses of directly measured quantities, reconstructed parameters and the reconstructed plasma contour have all been examined. Provided that the plasma position and shape perturbation were small enough for the linearity assumption to hold, agreement between the model and experiment was good. For some stimulations the open loop vertical position instability growth rate changed significantly. This led to oscillations in the vertical position that were unpredicted and illustrated the limitations of a linear model. A different model was developed with the assumption that the flux at the plasma boundary is frozen and the predictions of this model were also compared with experimental results. It proved not to be as reliable as the CREATE-L model for some simulation parameters, showing that the experiments were able to discriminate between different plasma response models. The closed loop response was also found to be sensitive to changes in the modelled plasma shape. It was not possible to invalidate the CREATE-L model, despite the extensive range of responses excited by the experiments.

A practical method for performing a tokamak equilibrium reconstruction in real time for arbitrary time varying discharge shapes and current profiles is described. An approximate solution to the Grad-Shafranov equilibrium relation is found which best fits the diagnostic measurements. Thus, a solution for the spatial distribution of poloidal flux and toroidal current density is available in real time that is consistent with plasma force balance, allowing accurate evaluation of parameters such as discharge shape and safety factor profile. The equilibrium solutions are produced at a rate sufficient for discharge control. This equilibrium reconstruction algorithm has been implemented on the digital plasma control system for the DIII-D tokamak. The first application of real time equilibrium reconstruction to discharge shape control is described.

A linear resistive magnetohydrodynamic (MHD) analysis of current driven instabilities in the reversed field pinch is presented. The presence of multiple resistive walls is taken into account using appropriate boundary conditions. A qualitative understanding of the effect of two walls, together with an approximate formula for the growth rate, is given by studying a simple skin pinch model. In particular, it is found that the mode growth rate is influenced by both wall time constants only for intermediate values of r_w (the position of the outermost shell). More realistic equilibria are then analysed, comparing the stability results obtained with an ideal or resistive wall with those with two resistive walls. It has been found that all the modes considered (m = 0 and m = 1) are sensitive to the wall resistivity and position, but the growth rates are reduced (even strongly in some circumstances) by the presence of a relatively `thin' wall at the plasma edge. Finally, a comparison between the experimental results and the linear theory predictions in terms of marginally stable states is given.

The magnetic field null conditions for plasma startup in DIII-D are established using a multipole expansion of the flux contribution from each element of the poloidal coil set to compute the vacuum magnetic field in real time using the measured coil currents. The use of this procedure has improved the breakdown conditions, as evidenced by the formation of the current channel with a toroidal electric field as low as 0.4 V/m without RF assistance. This represents a significant improvement over previous normal operation. Improved null conditions enhance the sensitivity of the minimum loop voltage to the wall conditions of the vacuum vessel. Results relating the breakdown voltage to carbon impurities are presented. It is shown that the observed difference between the radius of the poloidal field null and the radius of plasma initiation is a manifestation of finite aspect ratio, explained by the variation of the electric potential along the field line from the breakdown region to the wall.

The erosion yield of carbon by chemical hydrocarbon generation is investigated using spectroscopic particle flux measurements in the divertor of the ASDEX Upgrade tokamak. The methane formation at the graphite surface in hydrogen and deuterium plasmas is derived from CH/CD molecular band emission, and the corresponding hydrogenic fluxes are obtained from H_β/D_β spectroscopy, supported by Langmuir probe measurements in many cases. Under conditions of high particle flux densities above 10²² m^-2·s^-1, which are typical for high recycling divertor operation, a strong decrease of the apparent chemical erosion yield derived from CH release with increasing hydrogen flux density (and decreasing impact energy) is observed, Y_CH ∝ Γ_H^-0.8. The erosion yields depend on the hydrogen isotope; the values for deuterium are about a factor of 2 higher than those for hydrogen but exhibit the same flux dependence. These results are obtained for relatively low target temperatures between 300 and 360 K; the electron temperature at the target for the lowest yields/highest fluxes is about 5 eV. The yields at the highest fluxes are much lower than the results obtained from extrapolation of laboratory experiments performed under low flux density conditions. Three explanations are possible for the observed reduction of CH fluxes with increasing hydrogen flux densities: the flux dependence of the underlying chemical erosion yield Y_chem, the energy dependence of Y_chem entering via the experimental correlation of E and 1/Γ, and the plasma parameter dependence of the used molecular photon efficiency arising from the increasing prompt redeposition of CH₄ fragmentation products with rising Γ_H.

The Tokamak Simulation Code (TSC) has been used to model a new method of feedback stabilization of the axisymmetric instability in tokamaks using driven halo (or scrape-off layer) currents. The method appears to be feasible for a wide range of plasma edge parameters. It may offer advantages over the more conventional method of controlling this instability when applied in a reactor environment.

Report on the Thirteenth International Conference held at the Naval Postgraduate School, Monterey, California, United States of America, 13-18 April 1997.

Corrections to Nuclear Fusion 37 (1997) 1741